What are prime and composite numbers?

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Quick Answer

A prime number is a whole number greater than one that is only divisible by one or itself without leaving a remainder. A composite number is a whole number greater than one that is evenly divisible by more than one and itself.

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Examples of prime numbers include 11, 13, 29, 61 and 67. Each of these numbers is only divisible by one and itself without remainders. Examples of composite numbers include 12, 14, 28, 68 and 70. Each of these numbers has more divisors than one and itself that do not leave remainders.

One is not considered a prime or composite number. Fractions are not included when discussing prime and composite numbers because the focus is on whole numbers exclusively. Prime and composite numbers are considered to be a part of the fundamental theorem of arithmetic.

The fundamental theorem of arithmetic, or unique-prime-factorization theorem, says that all whole positive numbers greater than one are either prime numbers or the product of prime numbers. Many composite numbers are often factored down to their prime number factors to aid in solving problems. It is because of this that prime numbers are generally considered to be the basic building blocks of positive numbers.